An average brain neuron takes its inputs from an _average_ of 7000 other neurons, with the max being somewhere around 10k,
Purkinje cells in the cerebellum have sum up about 100k inputs. Purkinje cells are the sole output of the cerebellar cortex. And the cerebellum has as many neurons as the rest of the brain (~10^10). So your point is very valid, just an order of magnitude or so short on the estimate.